Resolution- versus sensitivity-effective diameter in pinhole collimation: experimental verification

Abstract

To account for photon penetration, the formulae used to calculate the geometric resolution of a pinhole collimator use an effective diameter d(e) rather than the physical diameter of the aperture. The expressions commonly used for d(e), however, were originally derived to include penetration in sensitivity calculations. To predict the full width at half maximum (FWHM) resolution of the point-spread function (PSF) of a knife-edge pinhole collimator, we have previously proposed simple expressions for a resolution-effective diameter d(re). Unlike those for d(e), expressions for d(re) predict both a dependence on the polar angle of the source (theta) and a non-isotropic PSF. In this paper, the new theory was tested by measuring experimentally the FWHM of the PSF. Results confirm the theoretical predictions that (a) d(re) provides the best estimates of the experimental FWHM as a function of theta and of the direction in the plane of the pinhole, (b) Paix's expression for d(e) tends to overestimate the FWHM, (c) Anger's is a better approximation, but still cannot predict the dependence on theta, and (d) the FWHM decreases with decreasing theta, i.e. resolution improves for sources at the edge of the field-of-view.